Symmetry of functions

Part 1 book "Foundations of geometric continuum mechanics" includes content: The elasticity problem; symmetry and dynamics, banachable spaces of sections of vector bundles over compact manifolds; manifolds of sections and embeddings; the general framework for global analytic stress theory; dual spaces corresponding to spaces of differentiable sections of a vector bundle - localization of sections and functionals; de rham currents; interlude - singular distributions of defects in bodies, vector valued currents; the representation of forces by stresses and hyperstresses,.... and other contents.

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This global minimum structure has the shape of a tetragonal bipyramid having two Sc atoms at two tops of pyramids binding with one edge of Ge-Ge. The ground electronic state of the global minimum isomer is the 2B2 state in the C2v symmetry. The most stable isomer of Sc2Ge6 − has been used to study the CO adsorption. The calculated results indicate that the Sc2Ge6 − cluster has a good interaction with the CO molecule. The adsorption positions are around the Sc atom with two stable models include adsorbing the C atom and adsorbing both the C and O atoms of the CO molecule.

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Part 1 book "A stroll through quantum fields" includes content: Basics of quantum field theory, functional quantization, path integrals for fermions and photons, non abelian gauge symmetry, renormalization of gauge theories, quantization of yang mills theory, renormalization group.

264p muasambanhan07 08-02-2024 0 0   Download

Ebook "Principles of protein X-Ray crystallography (Third edition)" provides the theoretical background necessary to understand how the structure of proteins is determined at atomic resolution. It is intended to serve as an introduction for graduate students, postdoctoral researchers, and established scientists who want to use protein crystallography in their own endeavors, or need to understand the subject in order to critically evaluate the literature.

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Part 1 of ebook "Group theory applied to chemistry" provides readers with contents including: Chapter 1 - Operations; Chapter 2 - Function spaces and matrices; Chapter 3 - Groups; Chapter 4 - Representations; Chapter 5 - What has quantum chemistry got to do with it;...

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Ebook Literary study: Part 1 includes contents: Transformative learning - mine and theirs; Making the case for discipline-based assessment; Where has assessment been in the modern language association? A disciplinary perspective; Measuring the humanities: the slippery slope from assessment to standardization; The pygmies in the cage: the function of the sublime in longinus; Approaching the ineffable: flow, sublimity, and student learning; Fearful symmetries: rubrics and assessment; Posthumanist measures: elephants, assessment, and the return of creativity; Assessment in literary education.

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Lecture Human-Computer interaction - Lesson 39: Behavior & form (Part 7). The main topics covered in this chapter include: principles of visual interface design, principles of information design, use of text and color in visual interfaces, consistency and standards,...

42p wangziyi_1307 26-04-2022 10 3   Download

A new method is developed for calculating the vibration-rotation-tunneling spectra of molecular clusters consisting of rigid monomers. The method is based on generation of optimized bases for each monomer. First, a sequential symmetry adaptation procedure is developed for relating the symmetries of monomer basis functions with the symmetries of the eigenstates of the cluster. Then this symmetry adaptation procedure is used in the generation of optimized bases and combining them for finding the eigenstates.

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Increased body mass index (BMI) has been associated with poorer function in patients who have undergone anterior cruciate ligament (ACL) reconstruction. However, the effect of high BMI on muscle strength in these patients remained unclear.

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The use of knee braces early after anterior cruciate ligament (ACL) reconstruction is a controversial issue. The study preliminarily compares the effect of a traditional brace blocked in knee extension and a new functional brace equipped with a spring resistance on walking and strength performance early after ACL reconstruction performed in the acute/subacute stage.

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Optimized geometries, formation energy, phonon spectra, electronic band structure, and elastic tensor calculation has ensured the energetically, dynamical and mechanical stability for the sheets. Furthermore, the theoretically found nanosheet series possess an intrinsic wide direct band gap preserving from wurtzite tetragonal-based bonding. This high symmetry wide bandgap semiconductor nanosheet series and their derivatives are expected to have broad applications in photocatalysis, and biomedicine.

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Bismuth dioxide selenide, Bi2O2Se, is a thermoelectric material that exhibits low thermal conductivity. Detailed understanding of the compounds band structure is important in order to realize the potential of this narrow band semiconductor. The electronic band structure of Bi2O2Se is examined using first - principles density functional theory and a primitive unit cell. The compound is found to be a narrow band gap semiconductor with very flat bands at the valence band maximum (VBM). VBM locates at points off symmetry lines. The energy surface at VBM is very flat.

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It is well-known that some famous probability density functions (PDF) of random variables are associated with symmetries of these random variables. The Boltzmann and Gaussian PDFs that are invariant under translation and spherical transformations of their variables, respectively, are obvious and well-studied examples reflecting not only symmetries of many physical phenomena but also their underlying conservation laws.

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In this paper, we only focused on consider phenomenon of spontaneous symmetry breaking in the case of space dependent coupling. The results show that in the case of a coupling between the two rings is a function of single-Gaussian symmetry breaking only between rings. In contrast, in the case of a coupling between them as a double-Gaussian function, the symmetry breaking occurs only in each ring, breaking the symmetry of the space dependent coupling.

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Affine periodicity is a generalization of the notion of conventional periodicity and it is a symmetry property for classes of functions. This study is concerned with the existence of (Q, T)-affine periodic solutions of discrete dynamical systems. Sufficient conditions for the main results are proposed due to discrete exponential dichotomy and fixed point theory.

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In the present paper, the Sawada–Kotera equation is considered by Lie symmetry analysis. All of the geometric vector fields to the Sawada–Kotera equation are obtained, and then the symmetry reductions and exact solutions of the Sawada–Kotera equation are investigated. Our results show that symmetry analysis is a very efficient and powerful technique in finding the solution of the proposed equation.

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In this note, higher order self-adjoint differential expressions on time scales, and associated with them self-adjoint boundary conditions, are discussed. The symmetry peoperty of the corresponding Green’s functions is emphasized.

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Let (M,g) be a smooth compact 3 ≤ n-dimensional Riemannian manifold, and G a subgroup of the isometry group of (M,g). We establish the best constants in second-order for a Sobolev inequality when the functions are G-invariant.

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Neutrino masses and mixing in an extended standard model acquiring an A4 flavor symmetry are considered. The corresponding three-neutrino mixing matrix obtained via a perturbative method allows us to determine the Dirac CP violation phase (δCP) as a function of the mixing angles (θ12,θ23,θ13). Then, numerical values and distributions of δCP are given. The latter values are quite close to the global fits of the experimental data for both the normal ordering and inverse ordering of the neutrino masses.

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The twonucleotide-bindingdomains (NBDs)of anumberof ATP-binding cassette (ABC) transporters have been shown to be functionally dissimilar, playing different roles in the transport process. A high degree of co-operativity has been determined for the NBDs of the human multidrug trans-porter, P-glycoprotein. However, the issue of functional symmetry in P-glycoprotein remains contentious.

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